Accurate simulation of turbulent flow is a common problem in engineering and academic fields. In this paper, the idea of data-driven turbulence modeling is adopted, and a framework of flow field inversion based on discrete adjoint is established. The SA model is modified by multiplying the production term of its eddy viscosity transport equation and a coefficient with non-uniform distribution, which is inferred with limited observation data. To improve the efficiency of discrete adjoint optimization under physical constraints, the constraint-augmented adjoint method is used, and its efficiency is verified in this paper. Two cases of iced airfoil and periodic hill are selected for analysis. The results obtained in both cases are highly consistent with the observed data, and the limited observation information can be generalized to the whole flow field with the help of the correction of the turbulence model. The analysis shows that the correction region deduced from field inversion has a certain physical significance and can guide further development of the turbulence model.
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